By Catherine Hoven

The use of the array to show two-digit multiplication was quite the discussion last night at my house.  My son, who is in grade 4, had math homework involving the calculation of area, and he decided to complete this when he was tired and should have been going to bed.  He solved the first few questions quite easily because he was able to multiply in his head or was able to skip count quite easily.  However, he then came to a rectangle with the dimensions of 18 and 7.  He knew that he needed to multiply the two numbers, but was unable to simply skip count or do this in one step.  So I watched him stack the numbers, but he wasn’t quite sure what to do with 56 from 8 x 7.   I then suggested to him to break the numbers apart.  I asked, “what is 18.” He said that 18 was 1 group of 10 and 8 more, but still couldn’t see his next step. He was tired and cranky by this time,so we put the math away and proceeded to get ready for bed.

As I was lying down with him tucking him in for the night, I picked up his booogie board (cool stylus board that erases with a button touch) and drew a building with many glass windows. We talked about the different ways that we could “see” the windows.  We then played eye-spy with arrays – from Lego stacks, to tiles, marshmellow peeps, to calendar squares etc.  It is surprising how many arrays you can find in a child’s bedroom!  I then saw a larger Lego flat rectangle.  My son loves Lego and is quite strong with visual spatial tasks.  Thinking of his frustration trying to represent the earlier area problem in a meaningful manner in his head, I asked him how he could cover the flat base with other lego flat pieces.  He quickly took the Lego piece and said “like this, like this, like this etc” covering up various sections with his hands to show the multiple flats that it would take to cover the entire surface. He then looked at me and said with a knowing smile, “you tricked me into doing math!”  I smiled back, and he said “I can finish the area tomorrow, it is just like building Lego. This is fun!”  So although he went to bed later than usual, I think that he feel asleep as a confident math learner.

We need to know our learner,  be open to the possibilities around us, and gently lead students to their next step.  As Fosnot wrote, “ No matter how clearly it is explained, the ideas cannot be directly transmitted with language – the learner must construct them. My son’s last words tonight were, “Let’s do this tomorrow night with the largest Lego flat that we own – the big gray one!”  This one, by the way, is 48 x 48! Tomorrow will be a busy day!


Featured image by Iker Uteaga on Unsplash